Harvard SEAS March 30, 2012

Brian Hayes


Computation and the Human Condition

March, 1972

Front cover of The Limits to Growth, published March 1972.

Part 1. Computing the Future


Earth Day, 1970

Walt Kelly's Pogo celebrates Earth Day 1970 with the slogan 'We have met the enemy and he is us'.

Nerdy environmentalism

Since ours is a formal, or mathematical, model, it also has two important advtanges over mental models. First, every assumption we make is written in a precise form.... Second,... implications for the future behavior of the world system can be traced without error by a computer, no matter how complicated they become.

Limits to Growth, p. 22

Nerdy catastrophe

If the present growth trends in world population, industrialization, pollution, food production, and resource depletion continue unchanged, the limits to growth on this planet will be reached sometime within the next one hundred years. The most probable result will be a rather sudden and uncontrollable decline in both population and industrial capacity.

Limits to Growth, p. 23

ASCII infographics

Results of the 'standard run' of the World3 model.

World3, standard run

Results of the 'standard run' of the World3 model.

World3, double-resources run

Results of the 'standard run' of the World3 model.

Jay Forrester and Project Whirlwind

Jay Forrester and friends testing early modules of the Whirlwind computer.

A core memory

A plane of magnetic-core memory from the Whirlwind computer, on display at the Computer Museum in Mountain View, Calif.




Part 2. Unboxing World3

Starting simple...

From the world of population biology we have the Lotka-Volterra equations:

\begin{aligned} \frac{dx}{dt} & = x(\alpha - \beta y) \\ \frac{dy}{dt} & = -y(\gamma - \delta x) \end{aligned}

Two equations with four free parameters (\(\alpha, \beta, \gamma, \delta)\) describe a rich spectrum of behavior. In the absence of predators, the prey species would proliferate without limit, \(x \rightarrow \infty\). In the absence of prey, the predator species would die out, \(y \rightarrow 0\). But when you put them together, what you get is not (generally) a simple equilibrium. Instead the two populations enter into cyclic oscillations.

Graph of oscillating predator and prey populations, somewhat out of phase.

An agent-style simulation by http://jseed.sourceforge.net/.

Plumbing and wiring

The Lotka-Volterra equations encoded in a flow diagram in the style of system dynamcs..

The Lotka-Volterra model in the iconography of system dynamics, with valves, flows and reservoirs.

Like the schematic of an oil refinery

The plumbing and wiring diagram for the complete World3 model, drawn by Stephen Flanders in 1972.


Plumbing and wiring: a detail

A redrawn segment of the World3 plumbing, centered on the life-expectancy variable.

Levels and rates

Levels and rates section of the diagram.

Auxiliary variables

The wiry part of the plumbing and wiring diagram.

Knobs to twiddle

Graphical piecewise linear function relating industrial output per capita to crowding multiplier from industrialization.

Arbitrary functions represented by piecewise-linear "tables". (This one relates wealth to the effects of crowding on life expectancy.)

How many knobs?

The urge to elaborate

More combinatorial complication

The wiry part of the plumbing and wiring diagram.

Putting the pieces together

The drag-and-drop interface of the Stella simulation software.

If we were building hardware, we might work directly from the diagram of vats and valves. System dynamics software offers that option even in software: Drag-and-drop model building in Stella II.


A specimen of the DYNAMO programming language.

That was then...

Diagram of the j, k, l model of time in DYNAMO.

As time goes by

Cyclic updating of level, auxiliary and rate variables.

Topological sorting

Cyclic updating of level, auxiliary and rate variables, with the aux variables highlighted.

Causal loops

Section of the plumbing and wiring diagram that has an illegal cycle in the directed graph.

Causal loops

Section of the plumbing and wiring diagram that has an illegal cycle in the directed graph, with the loop traced in red.

Opening the loop

Part 3. The Human Predicament

What, me worry?

Results of the 'standard run' of the World3 model.

In the standard run of the World3 model, the peak year for wealth and well-being is somewhere near 2020—just around the corner. It's all downhill from there. Should we worry?


This sort of model is an attempt not to predict the future but to illustrate the basic dynamic tendencies of a complex system under alternate policies.

Meadows et al., Models of Doom, p. 217


System dynamics models suggest [that] sensitive control points for increasing the world-wide quality of life exist in the rate of generation of capital investment and in food production, but that expansion of industrialization and food output are the counter productive directions, both should be restrained. The common answer to world distress has been to increase industrialization and food production, but hope for long-term improvements probably lies in reducing emphasis on both.

Forrester, 1971

Forrester's dilemma

Forrester's graph of what we can foresee, and what we can change.

One can forecast future conditions in the region where action is not effective, and one can have influence in the region where forecasting is not reliable.

Forrester, 2007

Global warning

What about other kinds of models? Specifically, what about climate models?




We believe [World3] is unique among all mathematical and mental world models available to us today. But there is no reason to be satisfied with it in its present form. We intend to alter, expand, and improve it as our knowledge and the world data base gradually improve.

The Limits to Growth, 1972


Brian Hayes



Look for more on this theme in the May-June American Scientist.